Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Apply H0 with
λ x2 . x2 = c0301.. x0 x1 ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x3) x0 leaving 2 subgoals.
Let x2 of type ι be given.
Let x3 of type ι → ι be given.
Apply unknownprop_ca0a36340929f8b1169d3f8aa48084209d774d84897dd819d42815b7351bd2a1 with
x2,
x0,
x3,
x1,
∀ x4 . prim1 x4 x0 ⟶ prim1 (x1 x4) x0 leaving 2 subgoals.
The subproof is completed by applying H2.
Assume H3: x2 = x0.
Assume H4:
∀ x4 . prim1 x4 x2 ⟶ x3 x4 = x1 x4.
Apply H3 with
λ x4 x5 . ∀ x6 . prim1 x6 x4 ⟶ prim1 (x1 x6) x4.
Let x4 of type ι be given.
Apply H4 with
x4,
λ x5 x6 . prim1 x5 x2 leaving 2 subgoals.
The subproof is completed by applying H5.
Apply H1 with
x4.
The subproof is completed by applying H5.
Let x2 of type ι → ι → ο be given.
The subproof is completed by applying H1.